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Correlation Exponent

المؤلف:  Grassberger, P. and Procaccia, I.

المصدر:  Measuring the Strangeness of Strange Attractors." Physica D 9

الجزء والصفحة:  189-208

15-9-2021

2108

Correlation Exponent

A measure  of a strange attractor which allows the presence of chaos to be distinguished from random noise. It is related to the capacity dimension  and information dimension , satisfying

(1)

It satisfies

(2)

where  is the Kaplan-Yorke dimension. As the cell size goes to zero,

(3)

where  is the correlation dimension.

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REFERENCES:

Grassberger, P. and Procaccia, I. "Measuring the Strangeness of Strange Attractors." Physica D 9, 189-208, 1983.